Coordinate converter using multiplying digital-to-analog converters

ABSTRACT

A coordinate converter used in a display system for generating deflection voltages capable of rotating and/or translating one or more images on the screen of a cathode ray tube is described. More particularly, the converter uses four multiplying digital to analogue converters each of which combines one analogue voltage representing one of the initial coordinates, x or y, with one binary digital input in two&#39;&#39;s complement form which represents either the sine or the cosine of the rotation angle. The outputs of these converters are combined to solve the coordinate rotation equations. Incremental voltages representing the desired translation may be added before and/or after the rotation computation.

United States Patent [72] inventors Roy M. Williams, ,lr.;

John R. Longland, Nashua, N.l-l. [21] Applv No. 811,092 [22] Filed Mar.27, 1969 [45] Patented Jan. 26, 1971 [7 3] Assignee Sanders Associates,Inc.

Nashua, N.H. a corporation of Delaware [54] COORDINATE CONVERTER USINGMULTIPLYING DIGlTAL-TO-ANALOG CONVERTERS 6 Claims, 6 Drawing Figs.

[52] U.S.Cl ..235/150.52, 340/347; 235/189 [51] lnt.Cl G06j 1/00, 606g7/22 [50] Field of Search 235/186, 189, 190, 191, 192, 197, 150.53;340/347A-D, D-A

[56] References Cited UNTTED STATES PATENTS 2,966,302 12/1960 Woo1feta1. 235/150.52

Primary ExaminerMalcolm A. Morrison Assistant Examiner-Joseph F.Ruggiero Attorney-Janis Etlinger ABSTRACT: A coordinate converter usedin a display system for generating deflection voltages capable ofrotating and/or translating one or more images on the screen of acathode ray tube is described. More particularly, the converter usesfour multiplying digital to analogue converters each of which combinesone analogue voltage representing one of the initial coordinates, x ory, with one binary digital input in two's complement fonn whichrepresents either the sine or the cosine of the rotation angle. Theoutputs of these converters are combined to solve the coordinaterotation equations. Incremental voltages representing the desiredtranslation may be added before and/or after the rotation computation.

COMPARE REF W Km m 6 2 m D E l N E. T A P NHO DISPLAY GENERATOR UNIT "-IOI' FIG. I

BllTAL C(ONTROLLER DISPLAY PROCESSOR UNIT ANALOG SIGNAL SOURCE REG.

TA x; r

"REG.

sm 8 c059 7 COORDINATE CONVERTER FIGfZ ANALOG GENERATOR l5- FUNCTIONsign -xc os9 I 46 FIG. 5

x: 3 C050 y sin 6 IINVE/VTORS ROY M. WILLIAMS JR.

JOHN R. LONGLAND BYVK FIGB

ATTORNEY COORDINATE CONVERTER USING MULTIPLYING DIGITAL-TO-ANALOGCONVERTERS BACKGROUND OF THE INVENTION 1. Field of the Invention Thisinvention relates generally to display systems which exhibit variouspatterns including images and characters on a viewing screen such as theface of a cathode ray tube. The invention relates more particularly toapparatus which enables one or more or all of the images or charactersto be translated and/or rotated to a new position and/or orientation onthe viewing screen.

One common type of display apparatus, with which the present inventionis particularly useful, is one in which various characters, symbols andimages, such as numbers, letters, circles, and/or pictorial images suchas those from television or radar equipment, may be displayed at anyposition or orientation on a viewing screen in response to commands froma computer or other directing device. Such characters and images may beformed one at a time by moving a cursor over the appropriate part of thescreen to trace the character or image. When one character is completed,the cursor is blanked out, moved to the next location, turned on, andmoved to trace out the next character. The programs of deflectionvoltages for forming frequently used characters may be sorted in anappropriate memory. The viewing screen normally has a short persistenceand the entire display is refreshed by retracing each character andimage frequently, for example, 60 times per second.

Display apparatus as generally described above is used for manydifferent purposes in many different environments. It has been founddesirable in many cases to be able to alter the view presented bychanging the position or orientation, or both, of the entirepresentation or any selected part thereof. For example, it may bedesired to move one character from the upper right to the lower left, inwhich case translation is required. As another example, it may bedesired to rotate the entire display about the center, in which casecoordinate rotation is required. Additionally, it is often useful to beable to both rotate and translate one or more selected characters inwhich case coordinate rotation and translation are both required.

2. Description of the Prior Art In the past, coordinate translation androtation has been obtained in various ways. For example, the waveformsfor generating characters in several orientations can be stored, butthis uses valuable memory space. As another example, the deflectioncoils of a cathode ray tube may be mechanically rotated, but this iscumbersome at best. Also, various combinations of coordinate translatorsand rotators have been proposed, but, as far as applicants are aware,none has been entirely satisfactory.

It is a general'object of the present invention to provide an improvedcoordinate converter for use with display apparatus.

Another object is to provide a coordinate converter which enables animage to be translated or rotated or both.

Another object is to provide a coordinate converter which enables animage to be translated either before or after being rotated.

Another object is to provide a coordinate converter enabling the imageto be rotated through a full 360 or any part thereof.

SUMMARY OF THE INVENTION Briefly stated, the coordinate rotation portionof the converter accepts two analogue signals representing theinstantaneous x and y coordinates of a point. It also accepts twodigital signals, in two's complement form, representing the sine andcosine of the angle of rotation. Four multiplying digital to analogueconverters are provided in which both x and y are multiplied by both thesine and the cosine of the angle. The result, depending upon thequadrant of the angle, may represent 1: or y multiplied by the absolutevalue of the trigonometric function or may represent x or y multiplied'by one minus the absolute value of the function. Additionally, eachmultiplying digital to analogue converter generates a signal accordingto the sign of the function, zero if the sign is positive, and thenegative ofx or y, as the case may be, if the sign of the functionisnegativc. The signals generated by the multiplying digital to analogueconverters are combined to derive two signals representing theinstantaneous coordinates of the point as rotated through the givenangle.

Analogue signals indicative of the incremental values of x and y fortranslation may be added to the x and y signals either before or aftermodification by the coordinate rotator.

BRIEF DESCRIPTION OF THE DRAWING For a clearer understanding of theinvention, reference may be made to the following detailed descriptionand the accompanying drawing, in which:

FIG. I is a schematic block diagram of a display system; connectionsFIG. 2 is a schematic block diagram of the coordinate converter and itsconnections to the remainder of the display system;

FIG. 3 is a schematic diagram useful in explaining the invention,

FIG. 4 is a schematic block diagram of the coordinate converter;

FIG. 5 is a schematic diagram of one of the multiplying digital toanalogue converters; and

FIG. 6 is a view of a portion of the apparatus of FIG. 4 withexplanatory matter added which is useful in explaining the invention.

DESCRIPTION OF PREFERRED EMBODIMENT Referring first to FIG. 1, there isshown a Display Indicator Unit 8 including the viewing screen 9 of acathode ray tube on which are displayed various characters, symbols,pictures, and the like. The Unit 8 may be but one of many similar oridentical devices, all of which may be controlled by the same DisplayGenerator Unit 10. Display Processor Unit l1, and Analogue Signal SourceI2. The source 12 represents schematically a source of signals which areprimarily pictorial in nature, such as those from a radar installationor a television camera. These signals, analogue in form, are applied tothe unit I0 so that they may be displayed if desired. The DisplayProcessor Unit 11 may be, and preferably is, a digital computerincluding equipment for receiving, storing, selecting and processinginformation regarding the time and location on the screen at whichvarious characters, symbols, etc. are to be displayed. Suitable signalsindicative of this information are applied to the display generator unit10 which responds thereto and, generally speaking, generates, andapplies to the unit 8, analogue signals indicative of the instantaneouscoordinates x and y and intensity z. The unit 10 of necessity includesconsiderable equipment, some of which is of particular interest forpresent purposes and is shown in FIG. 2.

Referring now to FIG. 2, there is shown the coordinate converter 14 ofthe present invention, a groupof analogue function generators l5, and adigital controller 16 including several registers l7, l8 and 19. Amongother things, the digital controller 16 applies suitable digital signalsto the function generators 15 to enable them to generate analoguevoltages indicative of the instantaneous values of the coordinates x andy. The digital controller 16 also generates signals indicative of (1)whether and by how much the instantaneous coordinates are to be rotated.These signals operate in conjunction with the register I7 to generatetwo signals indicative of the instantaneous values of the sine andcosine respectively of the angle through which the coordinates are to berotated. Each signal is in the well-known parallel binary digital two'scomplement form in which the most significant digit represents the signof the function, zero for positive and one for negative, while theremainder of the digits represent the absolute value of the function, ifpositive, and the absolute value of the complement, if negative. Thedigital controller 16 also generates signals indicative of (2) whetherand by how much the coordinates are to be translated before rotation and(3) whether and by how much the coordinates are to be translated afterrotation. These latter two groups of signals operate in conjunction withthe register 18 and 19 respectively to generate digital signalsindicative of the instantaneous values of the increments to be added,before and after rotation respectively, to the x and y coordinates totranslate the display of the point to its new location. The signals fromthe register 17, 18 and 19 are applied to the coordinate converter 14.The converter 14 combines its various inputs in a manner to be fullyexplained and generates two analogue output voltages indicative of theinstantaneous coordinates of the point after the various rotations andtranslations, if any, have been performed.

Referring now to FIG. 3, there is shown schematically any point P in aplane having coordinates x, y. Let us assume that the point P is rotatedabout the origin through an angle 0. Its new position will be a point N.It can be shown by simple straightforward mathematics which need not bedetailed here that the coordinates x y of the point N in terms of X, yand are z =x cos 6-y sin 6 yce=$ sin 6+y cos 0 These equations are usedin the coordinate converter 14.

Referring now to FIG. 4, two unidirectional voltages, representing bytheir amplitude and sign the magnitude and sign of the instantaneouscoordinates of a point, are received on conductors 21 and 22respectively and applied to adding circuits 23 and 24 respectively. Twodigital inputs representing the increments to be added to the x and ycoordinates to effect translation before rotation are applied to digitalto analogue converters 25 and 26 respectively, the analogue outputs ofwhich are passed through isolating amplifiers 27 and 28 respectively andapplied to adding circuits 23 and 24 respectively. The outputs of thelatter circuits are applied to isolating and polarity reversingamplifiers 31 and 32 respectively to obtain voltages indicative of thenegative of the x and y coordinates as modified by the aforesaidtranslational increments, which voltages are designated .x, and y,respectively. Four multiplying digital to analogue converters 33, 34, 35and 36 are provided. The x, voltage from the amplifier 31 is applied tothe converters 33 and 35 while the y, voltage from the amplifier 32 isapplied to the converters 34 and 36. The aforementioned digital signalfrom the digital controller 16 indicative of cos 0 is applied to theconverters 33 and 36 while the similar signal indicative of sin 0 isapplied to the converters and 35.

Referring now to FIG. 5, which shows the converter 33 schematically, thex, voltage is applied to an input conductor 41 to which are connected aplurality of switches, one for each bit in the input representing cosine0. One switch designated 42, is connected to an output conductor 43,designated the sign output conductor, and is operated by the mostsignificant bit of the cosine 0 representation, that is, by the signbit, and is opened when this bit is zero and closed when this bit isone. Therefore, when the sign of cosine 6 is positive, the voltage ofconductor 43 is zero while when the sign of cosine 0 is negative, thevoltage of conductor 43 is indicative of -x,. Each of the otherswitches, designated collectively by the reference character 44, isoperated by a separate one of the remaining bits of cosine 6 and each isconnected through its individual resistor 45 to an output conductor 46,designated the product output conductor. The ohmic value of each of theresistors is selected in accordance with well-known principles so thatthe voltage of the conductor 46 is indicative of the product of x1 andthe absolute value represented by the bits of cosine 0 other than themost significant bit. Although the switches 43 and 44 have beenillustrated as if they were mechanical switches, as indeed they may be,it is preferred at present that they be fast acting switches such asdiode, transistor, or other solid state switches.

Referring again to FIG. 4, the converters 34, 35 and 36 are identical tothe converter 33 described in connection with FIG. 5. The outputs ofconverters 33 and 34 are combined to obtain an output indicative of xwhile the outputs of converters 35 and 36 are combined to obtain anoutput indicative of y More particularly, amplifiers 48 and 49 areprovided, each having first and second inputs designated plus and minusrespectively. A voltage applied to the minus input is reversed inpolarity and added to that applied to the plus input. The product outputof the.,converter 33 is combined in an adding circuit 51 with the signoutput of the converter 34 and applied to the minus input of theamplifier 48. The product output of the converter 34 is combined in anadding circuit 52 with the sign output of the converter 33 and appliedto the plus input of the amplifier 48. The product output of theconverter 35 is combined in an adding circuit 53 with the product outputof the converter 36 and applied to the minus input of the amplifier 49.The sign output of the converter 35 is combined in an adding circuit 54with the sign output of the converter 36 and applied to the plus inputof the amplifier 49. Additionally the digital inputs from the controller16 representing the increments to be added to the x and y coordinates toeffect translation after rotation are applied to digital to analogueconverters 56 and 57 respectively, the analogue outputs of which arepassed through isolating amplifier 58 and 59 respectively and applied tothe adding circuits 52 and 54 respectively. It will be understood thatthe adding circuits 5154 and the amplifiers 48 and 49 represent but. oneway, albeit that preferred at present, for combining the variousvoltages with the proper polarity.

Let it be assumed for the moment that there are no translationalincrements to be added and that the rotational angle 6 is in the firstquadrant so that both the sine and the cosine are positive. Then thesign outputs of all of the converters 33, 34, 35 and 36 are zero whilethe product outputs are voltages indicative of -x, cos 6, y,, sin 0, x,sin 0 and y cos 6 respectively. The combination in amplifier 48 of x,cos 6 with polarity reversal and -y, sin 0 without polarity reversalyields an output voltage indicative of x, as defined by equation (ISimilarly, the combination in amplifier 49 of -x, sin 6 and -y cos 6both with polarity reversal, yields as output voltage indicative of y asdefined by equation 2.

Let it next be assumed that the rotational angle 0 is in the secondquadrant so that sin 0 is positive while cos 6 is negative. As shown inFIG. 6, the sign output of converter 33 is a voltage indicative of x,and is applied through the adding circuit 52 to the plus input of theamplifier 48. The sign output of converter 34 is zero. The productoutput of converter 33 is a voltage indicative of x, (1- ]cos 0] and isapplied through the adding circuit 51 to the minus input of theamplifier 48. The product output of the converter 34 is a voltageindicative of -y [sin 6| and is applied through the adding circuit 52 tothe plus input of the amplifier 48. The sum of x, without polarityreversal, x, +x, [cos 0] with polarity reversal, and -y, [sin 6] withoutpolarity reversal yields a voltage indicative of Equation (3) is seen tobe identical to equation (1) when it is remembered that in the secondquadrant cos 0 is negative and sin 0 is positive. v

A similar analysis as to x and y for the remaining quadrants shows thatthe circuit of FIG. 4 yields correct results in all cases.

Referring again to FIG. 4, the output indicative of x,.c and y cappearing on conductors 61 and 62 respectively are voltages suitable forapplication to the deflection system of the display device 11 of FIG. 1.Additionally, an edge detecting arrangement is provided to generate asignal when either coordinate is large enough to deflect the beam beyondthe edge of the screen. More particularly, these voltages are applied toa comparing circuit 63 where each is compared with an appropriatereference voltage indicative of the signal required to place the beam ofthe tube at the edge of the screen. For example, if 5 volts plus orminus is required to place the beam at the horizontal edge, right orleft, and 4 volts plus or minus is required to place the beam at the topor the bottom, then xaand y c would be compared in absolute value with 5volt and 4 volt references respectively and a signal would be generatedwhen these values were exceeded. The signal can be used to takeappropriate action automatically or simply as a warning device for theoperator.

Although a preferred embodiment of the invention has been described inconsiderable detail for illustrative purposes, many modifications withinthe spirit of the invention will occur to those skilled in the art. Itis therefore desired that the protection afforded by Letters Patent belimited only by the true scope of the appended claims. We claim:

1. A multiplying digital to analogue converter, comprising:

means for receiving an analogue input;

means for receiving a digital input in twos complement form; means forgenerating a first analogue output which is alternatively zero orindicative of said analogue input, depending upon the most significantbit of said digital input; and

means for generating a second analogue output indicative of the productof said analogue input and the quantity represented by the remainder ofthe bits of said digital input. 2. A multiplying digital to analogueconverter in accordance with claim I in which the means for generatingthe first analogue output includes a switch connected to said analogueinput and operated in response to the most significant bit of saiddigital input.

3. A multiplying digital to analogue converter in accordance with claim2 in which the means for generating the second analogue output includesan output line, a plurality of resistors and a plurality of switches,each of said switches being operated in response to one of the remainingbits of said digital input and each arranged to selectively connect oneof said resistors between said analogue input and said output line. Y

4. Apparatus for deriving a unidirectional voltage the magnitude andsign of which are indicative of the function x cos y sin 0 where x and yare available as unidirectional analogue voltage inputs indicativethereof and sin 0 and cos 0 are available as binary digital quantitiesin twos complement form indicative thereof, comprising:

first and second multiplying digital to analogue converters, each forreceiving one of said analogue voltage inputs and one of said digitalquantities, each for generating a first analogue output voltage which isalternatively zero or indicative of the analogue voltage appliedthereto, depend ing upon the most significant bit of the digitalquantity applied thereto, and each for generating a second analogueoutput voltage indicative of the product of the applied analogue inputand the quantity represented by the remainder of the bits of the applieddigital quantity;

means for applying the negative of said voltage indicative of x and saidquantity indicative of cos 0 to said first multiplying digital toanalogue converter;

means for applying the negative of said voltage indicative of y and saidquantity indicative of sin 0 to said second multiplying digital toanalogue converter; and

means for summing said first output voltage of said first converter,said second output voltage of said second converter, the negative ofsaid second output voltage of said first converter and the negative ofsaid first output voltage of said second converter, whereby theresulting voltage is indicative of the function 1 cos 0 y sin 9.

5. Apparatus for deriving voltages indicative of the rectangularcoordinates of a point which has been rotated about the origin throughan angle 0 from an initial point having coordinates .r, y, comprising:A. First, second, third and fourth multi lyingdigital to analogueconverters,

. eac including means for receiving an analogue voltage input and adigital input in two's complement form;

2. each converter being for generating a first voltage output which isalternatively zero or indicative of the analogue inputdepending upon themost significant bit in said digital input; and

3. each converter being for generating a second voltage outputindicative of the product of said analogue input and the quantityrepresented by the remainder of the bits of said digital input;

B. means for applying the negative of an analogue voltage indicative ofx to said first and third converters and applying the negative of ananalogue voltage indicative of y to said second and fourth converters;

C. means for applying a digital quantity in two's complement formindicative of the cosine of 0 to said first and fourth converters andfor applying a digital quantity in twos complement form indicative ofthe sine of 0 to said second and third converters,

D. means for summing sald first output of said first converter, saidsecond output of said second converter. the negative of said secondoutput of said first converter and the negative of said first output ofsaid second converter, whereby a voltage indicative of the new xcoordinate is obtained, and

E. means for summing said first output of said third converter, saidfirst output of said fourth converter, the negative of said secondoutput of said third converter and the negative of said second output ofsaid fourth converter whereby a voltage indicative of the new ycoordinate is obtained.

6. A coordinate converter, comprising, first and second multiplyingdigital to analogue converters, each including:

means for receiving an analogue input;

means for receiving a digital input in two's complement form;

means for generating a first analogue output voltage which isalternatively zero or indicative of said analogue input, depending uponthe most significant bit of said digital input;

means for generating a second analogue output voltage indicative of theproduct of said analogue input and the absolute value of said digitalinput;

means for applying analogue inputs indicative of the negative of theabscissa and the negative of the ordinate of a point to said first andsecond converters, respectively;

means for applying digital inputs indicative of the sine and cosine ofan angle through which said point is to be rotated to said first andsecond converters, respectively; and

means for summing;

said first output of said first converter; said first output of saidsecond converter; the negative of said second output of said firstconverter; the negative of said second output of said second converter;and

whereby the sum is an analogue quantity indicative of the new ordinateof said point after rotation through said angle.

1. A multiplying digital to analogue converter, comprising: means forreceiving an analogue input; means for receiving a digital input intwo''s complement form; means for generating a first analogue outputwhich is alternatively zero or iNdicative of said analogue input,depending upon the most significant bit of said digital input; and meansfor generating a second analogue output indicative of the product ofsaid analogue input and the quantity represented by the remainder of thebits of said digital input.
 2. A multiplying digital to analogueconverter in accordance with claim 1 in which the means for generatingthe first analogue output includes a switch connected to said analogueinput and operated in response to the most significant bit of saiddigital input.
 2. each converter being for generating a first voltageoutput which is alternatively zero or indicative of the analogue inputdepending upon the most significant bit in said digital input; and 3.each converter being for generating a second voltage output indicativeof the product of said analogue input and the quantity represented bythe remainder of the bits of said digital input; B. means for applyingthe negative of an analogue voltage indicative of x to said first andthird converters and applying the negative of an analogue voltageindicative of y to said second and fourth converters; C. means forapplying a digital quantity in two''s complement form indicative of thecosine of theta to said first and fourth converters and for applying adigital quantity in two''s complement form indicative of the sine oftheta to said second and third converters, D. means for summing saIdFirst output of said first converter, said second output of said secondconverter, the negative of said second output of said first converterand the negative of said first output of said second converter, wherebya voltage indicative of the new x coordinate is obtained, and E. meansfor summing said first output of said third converter, said first outputof said fourth converter, the negative of said second output of saidthird converter and the negative of said second output of said fourthconverter whereby a voltage indicative of the new y coordinate isobtained.
 3. A multiplying digital to analogue converter in accordancewith claim 2 in which the means for generating the second analogueoutput includes an output line, a plurality of resistors and a pluralityof switches, each of said switches being operated in response to one ofthe remaining bits of said digital input and each arranged toselectively connect one of said resistors between said analogue inputand said output line.
 4. Apparatus for deriving a unidirectional voltagethe magnitude and sign of which are indicative of the function x costheta -y sin theta where x and y are available as unidirectionalanalogue voltage inputs indicative thereof and sin theta and cos thetaare available as binary digital quantities in two''s complement formindicative thereof, comprising: first and second multiplying digital toanalogue converters, each for receiving one of said analogue voltageinputs and one of said digital quantities, each for generating a firstanalogue output voltage which is alternatively zero or indicative of theanalogue voltage applied thereto, depending upon the most significantbit of the digital quantity applied thereto, and each for generating asecond analogue output voltage indicative of the product of the appliedanalogue input and the quantity represented by the remainder of the bitsof the applied digital quantity; means for applying the negative of saidvoltage indicative of x and said quantity indicative of cos theta tosaid first multiplying digital to analogue converter; means for applyingthe negative of said voltage indicative of y and said quantityindicative of sin theta to said second multiplying digital to analogueconverter; and means for summing said first output voltage of said firstconverter, said second output voltage of said second converter, thenegative of said second output voltage of said first converter and thenegative of said first output voltage of said second converter, wherebythe resulting voltage is indicative of the function x cos theta -y sintheta .
 5. Apparatus for deriving voltages indicative of the rectangularcoordinates of a point which has been rotated about the origin throughan angle theta from an initial point having coordinates x, y,comprising: A. First, second, third and fourth multiplying digital toanalogue converters,
 6. A coordinate converter, comprising, first andsecond multiplying digital to analogue converters, each including: meansfor receiving an analogue input; means for receiving a digital input intwo''s complement form; means for generating a first analogue outputvoltage which is alternatively zero or indicative of said analogueinput, depending upon the most significant bit of said digital input;means for generating a second analogue output voltage indicative of theproduct of said analogue input and the absolute value of said digitalinput; means for applying analogue inputs indicative of the negative ofthe abscissa and the negative of the ordinate of a point to said firstand second converters, respectively; means for applying digital inputsindicative of the sine and cosine of an angle through which said pointis to be rotated to said first and second converters, respectively; andmeans for summing; said first output of said first converter; said firstoutput of said second converter; the negative of said second output ofsaid first converter; the negative of said second output of said secondconverter; and whereby the sum is an analogue quantity indicative of thenew ordinate of said point after rotation through said angle.